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C₂²×#2429 #7627852

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

12426 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 20 points:

(1,2);(3,4);(9,10,11,12)(14,17)(15,19);(6,8)(9,10,11,12)(13,14)(15,18)(16,17)(19,20);(5,6)(7,8)(9,10)(11,12)(13,14)(15,18)(16,17)(19,20);(13,15,16,19)(14,18,17,20)

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7535048);